Answer: 39
39 is the only answer option greater than 17
The area of a trapezium is 156cm2, the parallel sides are 17cm and 35cm respectively. What is the height of the trapezium
Answer:
6 cm
Step-by-step explanation:
You want the height of a trapezium with bases 17 cm, 35 cm and area 156 cm².
Area formulaThe formula for the are of a trapezium is ...
A = 1/2(b1 +b2)h
Filling in the given values, we have ...
156 = 1/2(17 +35)h = 26h
6 = h . . . . . . . . . . divide by 26
The height of the trapezium is 6 cm.
Answer:
6cm
Step-by-step explanation:
To find:-
The height of the trapezium.Answer:-
We are here given that the area of the trapezium is 156cm² and two of the parallel sides are 17cm and 35cm .We are interested in finding out the height of the trapezium.
The area of the trapezium is given by the formula,
[tex]:\implies \sf Area =\dfrac{1}{2}\times (s_1+s_1)\times h \\[/tex]
where s1 and s2 are the || sides of the trapezium and h is the height of the trapezium.
Now on substituting the respective values in the given formula, we have;
[tex]:\implies \sf 156cm^2 =\dfrac{1}{2} (17cm+35cm)\times h \\[/tex]
[tex]:\implies \sf 156cm^2(2) = 52cm (h) \\[/tex]
[tex]:\implies \sf h =\dfrac{156(2)}{52} cm\\[/tex]
[tex]:\implies \sf \pink{ height = 6 cm }\\[/tex]
Hence the height of the trapezium is 6cm .
5 Mrs. Newsome bought a piece of fabric 142 centimeters long to make a quilt for her son's bedroom. She bought a piece of fabric 2 meters long for curtains. How could Mrs. Newsome find the total length, in centimeters, of both pieces of fabric? Multiply 2 by 2,000, then add 142. Add 2 and 142, then multiply by 100. Divide 142 by 100, then add 2,000. O Multiply 2 by 100, then add 142. B C
Answer:
Step-by-step explanation:
To find the total length of both pieces of fabric in centimeters, we need to add the length of the first piece of fabric (142 cm) and the length of the second piece of fabric (2 meters).
However, we need to make sure that the units are consistent before we add the lengths. We can convert the length of the second piece of fabric from meters to centimeters by multiplying by 100. Therefore, the total length in centimeters is:
142 cm + 2 meters * 100 cm/meter = 142 cm + 200 cm = 342 cm
The option that correctly gives the answer is "Multiply 2 by 100, then add 142" (Option C).
Question 4 X Suppose that starting today, you make deposits at the beginning of each quarterly period for the next 40 years. The first deposit is for 400, but you decrease the size of each deposit by 1% from the previous deposit. Using an nominal annual interest rate of 8% compounded quarterly, find the future value (i.e. the value at the end of 40 years) of these deposits. Give your answer as a decimal rounded to two places (i.e. X.XX).
if we make quarterly deposits and invest them at an nominal annual interest rate of 8% compounded quarterly for 40 years, we will have $143,004.54 at the end of the 40 years.
The first step in solving this problem is to calculate the amount of each quarterly deposit. We know that the first deposit is $400, and each subsequent deposit decreases by 1% from the previous deposit. This means that each deposit is 99% of the previous deposit. To calculate the size of each deposit, we can use the following formula:
deposit_ n = deposit_(n-1) * 0.99
Using this formula, we can calculate the size of each quarterly deposit as follows:
deposit_1 = $400
deposit_2 = deposit_1 * 0.99 = $396.00
deposit_3 = deposit_2 * 0.99 = $392.04
deposit_4 = deposit_3 * 0.99 = $388.12
...
We can continue this pattern for 40 years (160 quarters) to find the size of each quarterly deposit.
Next, we need to calculate the future value of these deposits using an nominal annual interest rate of 8% compounded quarterly. We can use the formula for compound interest to calculate the future value:
[tex]FV = PV * (1 + r/n)^(n*t)[/tex]
where FV is the future value, PV is the present value (which is zero since we are starting with deposits), r is the nominal annual interest rate (8%), n is the number of times the interest is compounded per year (4 since we are compounding quarterly), and t is the number of years (40).
We can substitute the values into the formula and solve for FV:
[tex]FV = $400 * (1 + 0.08/4)^(440) + $396.00 * (1 + 0.08/4)^(439) + $392.04 * (1 + 0.08/4)^(4*38) + ... + $1.64 * (1 + 0.08/4)^4[/tex]
After solving this equation, we get a future value of $143,004.54, rounded to two decimal places. This means that if we make quarterly deposits and invest them at an nominal annual interest rate of 8% compounded quarterly for 40 years, we will have $143,004.54 at the end of the 40 years.
This calculation highlights the power of compound interest over long periods of time. By making regular contributions and earning interest on those contributions, our investment grows exponentially over time. It also shows the importance of starting early and consistently contributing to an investment over time in order to achieve long-term financial goals.
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Question 2 (2 points) ✓ Saved
In the news, you hear "tuition is expected to increase by 12% next year." If tuition
this year was $5,500 per year, what will it be next year?
660
6160
4840
Cannot be solved.
Answer: 6,160
Step-by-step explanation:
Immediately, without even doing any math, the only logical answer would be 6160. This is because the current tuition is 5,500 and it is increasing so the answer cannot be lower.
However, mathematically you can prove this by turning 12% into a decimal and multiplying it by 5,500. 12% could be converted to .12 and because it is increasing you must add 1, or 100%, since that is what it started with. 5,500 x 1.12 = 6,160.
If r and s are constants and r² +rx + 12 is equivalent to (x+3)(x + 5), what is the value of r?
F.:3
H. 7
J. 12
K. Cannot be determined from the given information
Answer:
H. 7
Step-by-step explanation:
Given x² + rx + 12 is equivalent to (x + 3)(x + s), equate the two expressions and expand the right side of the equation:
[tex]\begin{aligned}x^2+rx+12&=(x + 3)(x + s)\\ x^2+rx+12&=x^2 + sx + 3x + 3s\\x^2+rx+12&=x^2 + (s+3)x + 3s\end{aligned}[/tex]
To find the value of r, first find the value of s.
The constant term of the right-hand side must be equal to the constant term of the left-hand side. Therefore:
[tex]\implies 3s = 12[/tex]
Solve for s by dividing both sides of the equation by 3:
[tex]\implies s = 4[/tex]
Compare the coefficients of the terms in x:
[tex]\implies r = s + 3[/tex]
Substitute the value of s into the equation and solve for r:
[tex]\begin{aligned} \implies r &= s + 3\\&= 4 + 3\\&= 7\end{aligned}[/tex]
Therefore, the value of r is 7.
Answer:
[tex]\large\boxed{\sf r = 7 }[/tex]
Step-by-step explanation:
Correct question:- If r and s are constants and r² +rx + 12 is equivalent to (x+3)(x + s), what is the value of r?
Here we are given that , the expression (x+3)(x+s) is equal to r² + rx + 12 .
Firstly, expand the expression (x+3)(x+s) as ,
[tex]\implies (x+3)(x+s) \\[/tex]
[tex]\implies x(x+s)+3(x+s) \\[/tex]
[tex]\implies x^2 + xs + 3x + 3s \\[/tex]
Take out x as common,
[tex]\implies x^2 + (3+s)x + 3s \\[/tex]
Now according to the question,
[tex]\implies x^2 + (3+s)x + 3s = r^2 + rx + 12\\[/tex]
On comparing the respective terms , we get,
[tex]\implies r = 3 + s \\[/tex]
[tex]\implies 3s = 12 \\[/tex]
Solve the second equation to find out the value of s , so that we can substitute that in equation 1 to find "r" .
[tex]\implies 3s = 12 \\[/tex]
[tex]\implies s =\dfrac{12}{3}=\boxed{4} \\[/tex]
Now substitute this value in equation (1) as ,
[tex]\implies r = 3 + s \\[/tex]
[tex]\implies r = 3 + 4 \\[/tex]
[tex]\implies \underline{\underline{ \red{ r = 7 }}} \\[/tex]
and we are done!
can someone help me please!
The median is the middle value of a data set when the values are arranged in order from lowest to highest (or highest to lowest). If there is an even number of values, then the median is the average of the two middle values. The median divides the data set into two halves, with half of the values being below the median and half of the values being above the median.
The first quartile, denoted as Q1, is the value that separates the lowest 25% of the data from the rest of the data. The second quartile, denoted as Q2, is the median of the data set. The third quartile, denoted as Q3, is the value that separates the lowest 75% of the data from the rest of the data.
The data-set has in this problem has two-halves of five elements, divided by the number 21, hence the median and the quartiles are given as follows:
The median of the data-set is of: 21 minutes.The lower quartile of the data-set is of 13 minutes. -> Median of the first five elements.The upper quartile of the data-set is of 27 minutes. -> Median of the last five elements.More can be learned about the median of a data-set at https://brainly.com/question/3514929
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a
21 units squared
b
27.6 units squared
c
32.2 units squared
d
42 units squared
The area of the right triangle given in this problem is given as follows:
21 units squared -> Option A.
How to obtain the area of a triangle?To calculate the area of a triangle, you can use the formula presented as follows:
Area = (1/2) x base x height
In which the parameters are given as follows:
"base" is the length of the side of the triangle that is perpendicular to the height."height" is the length of the perpendicular line segment from the base to the opposite vertex.For a right triangle, we can consider one side to be the base and the other side to be the height, hence the parameters are given as follows:
Base of 7 units.Height of 6 units.Hence the area of the triangle is given as follows:
A = 0.5 x 7 x 6 = 21 units squared.
Missing InformationThe complete problem is defined as follows:
"Calculate the area of the given triangle".
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The true statements are:
The graph of the function is a parabola.
The graph contains the point (0, 0).
The graph does not contain the point (20, -8).
How to deal with quadratic equation?The quadratic function is f(x) = x^2 - 5x + 12. Here are the statements that are true:
The value of f(-10) = 82:
To find f(-10), we substitute -10 for x in the function:
[tex]$$f(-10) = (-10)^2 - 5(-10) + 12 = 100 + 50 + 12 = 162$$[/tex]
Therefore, the statement "The value of f(-10) = 82" is false.
The graph of the function is a parabola:
Since the highest power of x in the function is 2, the graph of the function will be a parabola. Therefore, the statement "The graph of the function is a parabola" is true.
The graph of the function opens down:
The coefficient of [tex]$x^2$[/tex] in the function is positive (+1), which means the parabola opens upwards. Therefore, the statement "The graph of the function opens down" is false.
The graph contains the point (20, –8):
To see whether the point (20, -8) is on the graph of the function, we substitute x=20 into the function:
[tex]$$f(20) = (20)^2 - 5(20) + 12 = 400 - 100 + 12 = 312$$[/tex]
Since the y-coordinate of the point (20, -8) is not equal to 312, the statement "The graph contains the point (20, –8)" is false.
The graph contains the point (0, 0):
To see whether the point (0, 0) is on the graph of the function, we substitute x=0 into the function:
[tex]$$f(0) = (0)^2 - 5(0) + 12 = 12$$[/tex]
Since the y-coordinate of the point (0, 0) is equal to 12, the statement "The graph contains the point (0, 0)" is true.
Therefore, the true statements are:
The graph of the function is a parabola.
The graph contains the point (0, 0).
The graph does not contain the point (20, -8).
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Step-by-step explanation:
it was not clear if an average change rate would be sufficient, or if you needed an immediate change rate (as I also don't know if you covered derivatives already or not).
so, it would be helpful, if you could put a message to an answer that was not giving you what you need.
so, here now an answer for an immediate change rate (hopefully that is what you need) :
we have a right-angled triangle.
the direct line of sight (the direct distance between police and red car) is the Hypotenuse (the baseline opposite of the 90° angle).
the 50 ft and 180 ft are the legs.
Pythagoras gives us the length of the Hypotenuse :
Hypotenuse² = 50² + 180² = 2500 + 32400 = 34,900
Hypotenuse = sqrt(34900) = 186.8154169... ft
in general terms let's say x is the distance of the cop to the road, y is the distance on the road to the crossing point with the distance cop to road, and z is the line of sight distance between the red car and the cop (the Hypotenuse).
x² + y² = z²
now, the first derivative of distance is the change of distance = speed.
then dy/dt (= y') is how fast the car is traveling down the road. dx/dt (= x') is how fast the cop is traveling toward the road. and dz/dt (= z') is how fast the distance between the cop and the car is changing.
now, we take the derivative of our equation
x² + y² = z² with respect to time, variable by variable :
d(x² + y² = z²)/dt =
dx²/dx × dx/dt + dy²/dy × dy/dt = dz²/dz × dz/dt
that gives us the equation
2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)
x(dx/dt) + y(dy/dt) = z(dz/dt)
from the problem we know x (50 ft), y (180 ft), dz/dt (85 ft/s). we calculated z (the Hypotenuse = sqrt(34900), and since the cop is not moving, we know dx/dt = 0.
and we get
50ft×0ft/s + 180ft×(y') = sqrt(34900)ft×(85)ft/s
we solve for y' (the speed of the car on the road)
y' = sqrt(34900)×85/180 = 88.21839132... ft/s
≈ 88.22 ft/s
and now here the difference for an average change rate over the unrevealed of 1 second :
the radar measured the change of the distance (Hypotenuse) from 1 second ago to now.
so, 1 second ago, the distance was
186.8154169... + 85 = 271.8154169... ft
the 50 ft leg stays the same, but the 180 ft leg was (again via Pythagoras)
271.8154169...² = 50² + leg²
leg² = 271.8154169...² - 50² = 71,383.62088...
leg = 267.1771339... ft
so, the red car traveled
267.1771339... - 180 = 87.1771339... ft/s
as you can see, it is close, but there has to be a difference, as the average change rate is only an approximation to the immediate change rate.
Solve the following problems.
Given: AABC, DE AC,
BD DC, mZ1=m22,
mZBDC= 100°
Find: m< A, m< b , m
The value of the angles in the triangle are:
∠A = 60°, ∠B = 80° and ∠C = 40°
How to find the value of m∠A, m∠B, m∠C in the triangle?
We are given that BD = DC
Thus, ∠DBC = ∠BCD ---- 1 (angle in isosceles triangle)
We also have ∠BDC = 100°
In ΔBDC
∠BDC + ∠DBC + ∠BCD = 180° (sum of angles of triangle is 180°)
Using 1:
∠BDC + 2∠DBC = 180°
100° + 2∠DBC = 180°
2∠DBC = 180 - 100
2∠DBC = 80
∠DBC = 80/2
∠DBC = 40°
∠DBC = ∠BCD = ∠2 = 40°
Thus, ∠C = 40°
We are given that m∠1 = m∠2
Thus, ∠1 = ∠2 = 40°
Now, ∠BDC + ∠BDA = 180° (Linear pair)
100° + ∠BDA = 180°
∠BDA = 180 - 100
∠BDA = 80°
In ΔABD
∠ABD + ∠BDA + ∠BAD = 180° (sum of angles of triangle is 180°)
∠1 + ∠BDA + ∠BAD = 180°
40° + 80° + ∠BAD = 180°
120° + ∠BAD = 180°
∠BAD = 60°
So, ∠A = 60°
∠B = ∠1 + ∠2 = 40° + 40° = 80°
Therefore, ∠A = 60°, ∠B = 80° and ∠C = 40°
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Complete Question
m∠1=m∠2
D∈
AC
, BD = DC
m∠BDC = 100°
Find: m∠A, m∠B, m∠C
Assume the weight of a randomly chosen American passenger car is a uniformly distributed random variable ranging from 1,557 pounds to 4,665 pounds.(e) What is the probability that a vehicle will weigh between 1,946 and 4,455 pounds? (Round your answer to 4 decimal places.)
The probability that a vehicle will weigh between 1,946 and 4,455 pounds is 0.8076.
To solve this problem, we need to find the probability that a randomly chosen car weighs between 1,946 and 4,455 pounds. Since weight is uniformly distributed, we know that the probability density function is constant over the entire range of possible values.
First, we need to find the total range of possible values:
Range = maximum weight - minimum weight
Range = 4,665 - 1,557
Range = 3,108
Next, we need to find the range of values that fall between 1,946 and 4,455:
Target range = 4,455 - 1,946
Target range = 2,509
Finally, we can calculate the probability of a randomly chosen car falling within this target range:
Probability = Target range / Range
Probability = 2,509 / 3,108
Probability = 0.8076 (rounded to 4 decimal places)
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Find the Z-score for each of the following IQ scores
90 160(Einstein's IQ)
Answer:
z=3.75
Step-by-step explanation:
11/12 x 8/25 x 15/16 x 9/44
Sorry if photo is side ways or upside down
Help pleaseeeeeeeeee!
Answer:
y = 0.8x
Step-by-step explanation:
machine fills 24 jars in 30 seconds , then
fills 1 jar in [tex]\frac{24}{30}[/tex] = 0.8 seconds
thus number of jars filled in x seconds is
y = 0.8x
Which ordered pair maximizes the objective function p=3x+8y
(0,0)
(2,7)
(5,6)
(8,1)
Answer:
P(5,6) = 63
Step-by-step explanation:
Test each point to see which ordered pair maximizes the objective function:
(0,0): p = 3(0) + 8(0) = 0
(2,7): p = 3(2) + 8(7) = 6 + 56 = 62
(5,6): p = 3(5) + 8(6) = 15 + 48 = 63
(8,1): p = 3(8) + 8(1) = 24 + 8 = 32
Hence, (5,6) is the ordered pair that maximizes the objective function.
When I first look at an equation, HOW DO I KNOW which method to use to solve it?
for example:
-4(7j+2) = 10
What do I look for (by looking at it) to know if I should start to solve it by distributing, or just use division?
Please help! I am really confused. Thank you
Answer:
j = - 9/14
Step-by-step explanation:
-4(7j+2) = 10
Distributing First
-28j - 8 = 10
Try to get the variable on one side.
-28j = 18
Divide both sides by -28
j = -18/28 = - 9/14
LetY1,Y2,Yn denote a random sample of size n from a population whose density is given by f(y)={αyα−1θα,0≤y≤θ0,elsewhere,where α>0 is a known, fixed value, but θ is unknown. Consider the estimator ˆθ=max(Y1,Y2,...Yn).(a) Show that ˆθ is a biased estimator for θ.(b) Find a multiple of ˆθ that is an unbiased estimator of θ.(c) Derive MSE(ˆθ).
(a) θ is a biased estimator for θ.
(b) (α+1)Y/α is an unbiased estimator of θ.
(c) MSE(θ) = αθ^2/[(α+1)^2(α+2)]
(a) To show that θ is a biased estimator for θ, we need to show that E(θ) ≠ θ.
Using the definition of the maximum function, we have
P(θ ≤ y) = P(Y1 ≤ y, Y2 ≤ y, ..., Yn ≤ y) = (F(y))^n
where F(y) is the cumulative distribution function of Y.
Differentiating both sides with respect to y, we get:
f(θ) = n(F(θ))^(n-1)f(θ)
Simplifying, we get
F(θ) = (1/n)^(1/(n-1))
Using this result, we can find the expected value of θ
E(θ) = ∫₀^∞ θf(θ)dθ = ∫₀^θ θαθ^α-1dθ = αθ/(α+1)
Thus, E(θ) ≠ θ, which means that θ is a biased estimator for θ.
(b) To find a multiple of θ that is an unbiased estimator of θ, we can use the method of moments.
We know that the population mean of Y is
μ = ∫₀^θ yf(y)dy = αθ/(α+1)
The sample mean is
Y = (Y1+Y2+...+Yn)/n
Equating these two expressions and solving for θ, we get
θ = (α+1)Y/α
Thus, (α+1)Y/α is an unbiased estimator of θ.
(c) The mean squared error (MSE) of θ can be written as
MSE(θ) = E[(θ - θ)^2]
Expanding the square and using the linearity of expectation, we have
MSE(θ) = E[θ^2] - 2θE[θ] + E[θ]^2
We already know that E[θ] = αθ/(α+1).
To find E[θ^2], we can use the fact that θ = max(Y1,Y2,...Yn)
P(θ ≤ y) = P(Y1 ≤ y, Y2 ≤ y, ..., Yn ≤ y) = (F(y))^n
Differentiating both sides with respect to y, we get
f(θ) = n(F(θ))^(n-1)f(θ)
Using this result, we can find E[θ^2]
E[θ^2] = ∫₀^∞ θ^2f(θ)dθ = ∫₀^θ θ^2αθ^α-1dθ = αθ^2/(α+2)
Substituting these expressions into the MSE formula, we get
MSE(θ) = αθ^2/(α+2) - 2θ(αθ/(α+1)) + (αθ/(α+1))^2
Simplifying, we get
MSE(θ) = αθ^2/[(α+1)^2(α+2)]
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Can the binomial distribution be approximated by a normal distribution? n = 31, p = 0.9 Explain why or why not.
Therefore, we can use the normal distribution with mean 27.9 and standard deviation 1.67 to approximate the binomial distribution with n = 31 and p = 0.9.
What is binomial distribution?The binomial distribution is characterized by two parameters: the number of trials, denoted by n, and the probability of success on each trial, denoted by p. The probability of obtaining exactly k successes in n trials is given by the binomial probability mass function:
P(k) = (n choose k) * [tex]p^{k}[/tex] * [tex](1-p)^{(n-k)}[/tex],
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.
Given by the question.
Yes, the binomial distribution with n = 31 and p = 0.9 can be approximated by a normal distribution.
The conditions for a binomial distribution to be approximated by a normal distribution are as follows:
n*p >= 10
n*(1-p) >= 10
In this case, n = 31 and p = 0.9, so:
np = 310.9 = 27.9 >= 10
n*(1-p) = 31*0.1 = 3.1 >= 10
Condition 1 is satisfied, but condition 2 is not. Therefore, it is recommended to use a correction factor to improve the approximation.
The correction factor is given by:
[tex]\sqrt[2]{np(1-p)}[/tex]
Substituting the values, we get:
[tex]\sqrt[2]{310.90.1}[/tex]= 1.67
The corrected values for mean and standard deviation are:
mean = np = 310.9 = 27.9
standard deviation = [tex]\sqrt[2]{np(1-p)}[/tex] = 1.67
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1. In the figure below, solve for the missing side (seems harder then it should be)
A.7
B.8
C.9
D.10
Answer:
1. a square plus b square is c square where c is the hypotenuse.
so 1. 7^2 + 6^2 = c^2
49+36=c^2
85=c^2
the square root of 85 is c
9.22 is c
all the other questions are blurry :OO
Step-by-step explanation:
2.35 [5] <$2.9> For the following code: Ibu $t0,($t1) sw $t0,($t2) Assume that the register $t1 contains the address 0x10000000 and the data at address is 0x11223344. 2.35.1 [5] <$2.3, 2.9> What value is stored in 0x10000004 on a big-endian machine? 2.35.2 [5] <$2.3, 2.9> What value is stored in 0x10000004 on a little-endian machine?
The value stored in 0x10000004 on a big-endian machine is given by 0x00000011.
The word "endianness" refers to the arrangement of bytes as they are stored in computer memory. Endianness is classified as big or little depending on which value is stored first.
The "big end" (the most important item in the sequence) is put first and at the lowest storage address in a big-endian order. The "small end" (the least important item in the sequence) is put first in a little-endian order.
(1)In Big-endian Machine, first byte of multi-byte data will be stored first(at lower memory address)
Address Data
0x10000000 0x11
0x10000001 0x22
0x10000002 0x33
0x10000003 0x44
---------------------------------------------------------------------
lbu $t0, 0($t1)
Load unsigned byte in Register $t0 at address 0x10000000
Here byte at address 0x10000000 is 0x11
$t0 = 0x00000011
----------------------------------------------------
sw $t0, 0($t2)
Store a word(4 bytes) from Register $t0 to memory address 0x10000004
value stored in 0x10000004 is 0x00000011
--------------------------------------------------------------------------------
(2)In Little-endian Machine, last byte of multi-byte data will be stored first(at lower memory address)
Address Data
0x10000000 0x44
0x10000001 0x33
0x10000002 0x22
0x10000003 0x11
---------------------------------------------------------------------
lbu $t0, 0($t1)
Load unsigned byte in Register $t0 at address 0x10000000
Here byte at address 0x10000000 is 0x44
$t0 = 0x00000044
----------------------------------------------------
sw $t0, 0($t2)
Store a word(4 bytes) from Register $t0 to memory address 0x10000004
value stored in 0x10000004 is 0x00000044.
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Determine whether each of these functions from
Z
to
Z
is one-to-one (i.e., injective). (3 pts in total) (a)
f(n)=n−3
(b)
f(n)=n 2
−1
(c)
f(n)=n 5
The function f(n) = n - 3 maps distinct integers to distinct integers, and thus is injective.
(a) The function f(n) = n - 3 is one-to-one (injective). To prove this, suppose that f(a) = f(b) for some integers a and b. Then, we have a - 3 = b - 3, which implies a = b. Therefore, the function f(n) = n - 3 maps distinct integers to distinct integers, and thus is injective.
(b) The function f(n) = n^2 - 1 is not one-to-one (not injective). To see this, note that f(1) = f(-1) = 0, so different inputs map to the same output. In general, for any positive integer k, we have f(k) = f(-k), since (k^2 - 1) = ((-k)^2 - 1). Therefore, the function f(n) = n^2 - 1 is not injective.
(c) The function f(n) = n^5 is one-to-one (injective). To prove this, suppose that f(a) = f(b) for some integers a and b. Then, we have a^5 = b^5, which implies a = b (since the fifth root of a non-zero real number is unique). Therefore, the function f(n) = n^5 maps distinct integers to distinct integers, and thus is injective.
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Using a different map that is missing any indication of scale, you measure the distance from Point C
to Point D as five inches, but it is 500 miles on the ground. Prepare the following two expressions
of scale for the map:
(a) Fractional
(b) Written
SHOW YOUR WORK! This includes the potential for partial value, if incorrect.
Simplify your scale (e.g., reduce to 1 inch = x miles, not 5 inches = 250 miles).
Answer:
To calculate the scale of the map, we can use the following formula:
Scale = Actual distance / Map distance
(a) Fractional scale:
The actual distance between Point C and Point D is 500 miles, and the distance on the map is 5 inches. Therefore, the fractional scale can be calculated as:
Scale = 500 miles / 5 inches
Scale = 100 miles per inch
So the fractional scale of the map is 1 inch = 100 miles.
(b) Written scale:
To express the scale in written form, we can use the ratio of inches to miles. Since 1 inch represents 100 miles, we can write the scale as:
1 inch represents 100 miles
Alternatively, we can simplify the scale to a more common ratio by dividing both sides by 100:
1/100 inch represents 1 mile
Therefore, the written scale of the map is 1/100 inch = 1 mile.
divide 14 hours and 40 minutes by 5
you must give your answer in hours and minutes
Answer:
2 hours and 56 minutes.
Step-by-step explanation:
To divide 14 hours and 40 minutes by 5, we need to convert everything to minutes first.
14 hours is equal to 14 x 60 = 840 minutes.
So, 14 hours and 40 minutes are equal to 840 + 40 = 880 minutes.
Dividing 880 minutes by 5 gives us:
880 ÷ 5 = 176 minutes
Now, we need to convert the answer back to hours and minutes.
There are 60 minutes in 1 hour, so we can find how many hours are in 176 minutes by dividing by 60:
176 ÷ 60 = 2 with a remainder of 56.
So, the answer is 2 hours and 56 minutes.
6TH GRADE MATH PLS HELP TYSM
Answer:
m = 1
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-1,0) (0,1)
We see the y increase by 1 and the x increase by 1, so the slope is
m = 1
Last years freshman class at Big State university totaled 5,324 students
URGENT
The amount a student received in merit scholarships was $3,456 ($478 per student). The cost of full tuition was $4,200. This means that the difference between the amount of the scholarship and the cost of tuition was $744.
What is amount ?Amount is a numerical value that represents a quantity of something. It is used to measure the size, amount, or degree of something, often in terms of money, time, or distance. Amounts are usually expressed in a specific unit, such as dollars, minutes, or kilometers. Amounts can also refer to the total number of something, such as the amount of people in a room or the amount of items in a box. Amounts can also be used to describe a portion or percentage of something, such as the amount of a discount or the amount of interest earned.
To find the percentage of students who did not receive enough to cover full tuition, we need to divide the difference ($744) by the amount of the scholarship ($3,456). This gives us a percentage of 21.5%.
Rounded to the nearest whole percent, the answer is 22%. This means that 22% of students who received a merit scholarship did not receive enough to cover full tuition.
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f(s) = 3s + 2
p(s) = s^3+ 4s
Find (f • p)(-5)
The value of (f • p)(-5) is 1885 when functions are given as f(s) = 3s + 2 and p(s) = s³+ 4s.
What is function?In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is often represented by an equation or formula, and can be visualized as a graph. Functions are widely used in various areas of mathematics, science, engineering, and other fields to model real-world phenomena and solve problems.
Here,
f(s) = 3s + 2
p(s) = s³+ 4s
To find (f • p)(-5), we need to first find f(-5) and p(-5), and then multiply them together. To find f(-5), we substitute -5 into the function f(s) and simplify:
f(-5) = 3(-5) + 2
= -13
To find p(-5), we substitute -5 into the function p(s) and simplify:
p(-5) = (-5)³ + 4(-5)
= -125 - 20
= -145
Now we can multiply f(-5) and p(-5) together to find (f • p)(-5):
(f • p)(-5) = f(-5) * p(-5)
= (-13) * (-145)
= 1885
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HELP ASAP PLEASE! A yard plan includes a rectangular garden that is surrounded by bricks. In the drawing, the garden is 7 inches by 4 inches. The length and width of the actual garden will be 35 times larger than the length and width in the drawing.
What is the perimeter of the drawing? Show your work.
What is the perimeter of the actual garden? Show your work.
What is the effect on the perimeter of the garden with the dimensions are multiplied by 35? Show your work.
The perimeter of the garden in the drawing is 22 inches and the perimeter of the actual garden is 770 inches
The perimeter of the drawingThe perimeter of the garden in the drawing is calculated as
Perimeter of garden in drawing = 2(length + width)
So, we have
Perimeter of garden in drawing = 2(7 inches + 4 inches)
Evaluate
Perimeter of garden in drawing = 22 inches
So the perimeter of the garden in the drawing is 22 inches.
The perimeter of the actual gardenFor the perimeter of the actual garden, we have
Perimeter of actual garden = 22 inches * 35
Perimeter of actual garden = 770 inches
The effect on the perimeterWe can see that the perimeter of the actual garden is 35 times larger than the perimeter of the garden in the drawing.
This makes sense since the length and width of the actual garden are 35 times larger than the length and width in the drawing, so the perimeter (which is the sum of the lengths of all four sides) would also be 35 times larger.
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Which expressions are equivalent to 8(3/4y -2)+6(-1/2+4)+1
Answer: 6y + 6
Step-by-step explanation:
To simplify the expression 8(3/4y -2) + 6(-1/2+4) + 1, we can follow the order of operations (PEMDAS):
First, we simplify the expression within parentheses, working from the inside out:
6(-1/2+4) = 6(7/2) = 21
Next, we distribute the coefficient of 8 to the terms within the first set of parentheses:
8(3/4y -2) = 6y - 16
Finally, we combine the simplified terms:
8(3/4y -2) + 6(-1/2+4) + 1 = 6y - 16 + 21 + 1 = 6y + 6
Therefore, the expression 8(3/4y -2) + 6(-1/2+4) + 1 is equivalent to 6y + 6.
the solution set is
5r+20/10=3r-6/3
Answer:
r = -2
Step-by-step explanation:
5r + 20/10 = 3r -6/3
5r + 2 = 3r - 2
2r + 2 = -2
2r = -4
r = -2
Answer: r = -2
Step-by-step explanati